Abstract
In this paper, we consider iterative methods to find a simple root of a nonlinear equation f(x) = 0, where f : D∈R→R for an open interval D is a scalar function.
Highlights
One well-known 1-step iterative zero finding method, x n +1 = xn −f f (x n ),n '(x n ) (1)To derive (1), we approximate the given function f at x = xn by a linear function y of the form y(x) = a(x - xn )+b
In [8],a second-derivative-free method is obtained through approximating the second derivative f (y n ) in by
Noor and Khan [8] have used the same approximation of the second derivative (4) in (3) to suggest the following Iterative methods x n +1 =
Summary
One well-known 1-step iterative zero finding method, x n +1 Since (2) is the equation of the line tangent to f at x = xn , it is clear that Newton's method applied to f may be interpreted as a sequence of tangent lines with zeros converging to the zero of the function. Newton's method is a quadratically converging (p = 2) zero-finding algorithm. Where ξ is between xn and α https://rajpub.com/index.php/jam α xn+1 xn Figure ( 1.1 ) : A geometric interpretation of Newton's Method
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